In this paper, a digital control strategy based on equivalent fundamental and odd harmonic resonators is proposed for single-phase DVRs. By using a delay block, which can be equivalent to a bank of resonators, it rejects the fundamental and odd harmonic disturbances effectively. The structure of the single closed-loop control system consists of a delay block, a proportional gain and a set of zero phase notch filters. The principle of the controller design is discussed in detail to ensure the stability of the system. Both the supply voltage and the load current feedforwards are used to improve the response speed and the ability to eliminate disturbances. The proposed controller is simple in terms of its structure and implementation. It has good performances in harmonic compensation and dynamic response. Experimental results from a 2kW DVR prototype confirm the validity of the design procedure and the effectiveness of the control strategy.